Mathematical logician Kurt Gödel's work suggests that some mathematical statements are true even if they cannot be proven through internal logic, that every statement of even elementary logic can be both proved and disproved, and that the totality of mathematics cannot be perfectly and completely explained with the correct set of axioms. In vastly simplified terms, Gödel's completeness theorem (1929) states that every universally valid formula in first-order predicate calculus can be proved. This is not to be confused with Gödel's incompleteness theorem (1931), which states that no consistent system can be used to prove its own consistency.

Gödel was born in Brünn, Austria-Hungary (now Brno, Czech Republic), studied in Vienna, but fled Austria during the Nazi era and later refused all honors offered by the Viennese scientific community. He emigrated to the United States in 1940 and became an American citizen in 1948, though he stated that he had found logical inconsistencies in the US Constitution. He worked at the Institute for Advanced Study in Princeton, New Jersey, where he became best friends with Albert Einstein, who considered Gödel an intellectual equal and whose theories Gödel reformulated into a mathematical framework. The two men saw each other almost every day from the early 1940s until Einstein's death in 1955.

Gödel's effect on upper-echelon mathematics has been compared to that of René Descartes and Gottfried Leibniz, though remarkably, most of Gödel's work in mathematics was finished by the time he was in his mid-thirties. After that he published little, and his interest shifted to the deepest of philosophical questions.

It is perhaps an odd conundrum that despite his ability to hold, juggle, and rejigger the most complex and abstract mathematical and philosophical concepts, Gödel had a difficult time with more ordinary matters. After a bout of rheumatic fever in childhood he developed intense fears about his own health — hypochondria, some surmise — which grew worse in adulthood. He suffered at least two nervous breakdowns, and he was isolated from almost all aspects of life beyond the academic realm, except for a fascination with Walt Disney's film Snow White. He eventually grew concerned about germs or poisons in his food, to the point that he stopped eating and effectively starved himself to death.